On my new iPhone 5 I have mail notifications set up as on in the notification center, alert style is banners, badge app icon is on and show preview is on, view in lock screen is off. It is set up the same way as when I had an iPhone 4. However, when I get a new email and the phone's screen is not on, the next time I turn it on I will not get the banner alert, all I see is the badge icon. This is kind of annoying as I would like to see the banner to know who the email is from before going into the mail app.
The notifications for mail on my iPad running iOS 6 just like my iPhone 5 are set up the same way and work correctly.
Why would they not be working correctly on my iPhone 5?